Subgraphs and motifs in a dynamic airline network

How does the small-scale topological structure of an airline network behave as the network evolves? We analyse 15 years of data on Southwest Airlines’ domestic route network, focusing on the dynamics of small undirected subgraphs. Using exact enumeration formulae, we identify statistically over- and under-represented subgraphs (motifs and anti-motifs) and track their evolution. We uncover substantial topology transitions in network structure and provide evidence for time-varying power-law scaling between subgraph counts and the total number of edges. We also introduce a node-ranking measure that highlights node importance relative to specific local topologies. Our findings extend the toolkit of subgraph-based network analysis and offer new insight into transportation networks and the strategic behaviour of firms in oligopolistic markets.